Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#14267798 | C2 | semidirect |
| 3. #28385408 | C2 | semidirect |
| 4. #28385403 | C2 | semidirect |
| 6. C8×#14267798 | C2 | semidirect |
| 18. #20297725 | C4 | semidirect |
| 19. #20297724 | C4 | semidirect |
| 20. #20297723 | C4 | semidirect |
| 22. SD16×C449 | C4 | semidirect |
| 31. Dic898 | C2×C4 | semidirect |
| 36. #16813311 | C2×C4 | semidirect |
| 37. Q8×C449 | C2×C4 | semidirect |
| 39. C8×C449 | C2×C4 | semidirect |
| 48. #14267798 | SD16 | direct (N × H) |
| 58. C449 | C4×SD16 | semidirect |
| 73. SD16 | #14267798 | direct (N × H) |
| 85. Q8 | C2×#14267798 | semidirect |
| 98. C8 | C2×#14267798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14267798 | 2 |
| D4×#14267798 | 2 |
| #28385408 | 2 |
| #28385403 | 2 |
| #28385402 | 2 |
| C8×#14267798 | 2 |
| SD16×D449 | 2 |
| C4×SD16 | 449 |